When did Theseus first meet Hippolyta in A Midsummer Night's Dream?

In a Midsummer Night’s Dream by Shakespeare, the time when Theseus first met Hippolyta was not explicitly stated. However, the circumstance surrounding their meeting was mentioned in Act 1 Scene 1.

Hippolyta, I woo'd thee with my sword,
And won thy love doing thee injuries;

In the play, the statement by Theseus confirmed events in Greek mythology that described how Theseus first met Hippolyta. According to the myth, Theseus among other Greek heroes waged war upon the Amazons, a race of independent warrior women. Theseus fought against Hippolyta and defeated her in combat. He was also attracted to Hippolyta because she was queen of the Amazons. Theseus decided to marry her and make her queen of Athens. In this regard, Theseus first met Hippolyta during the war with the Amazons, as inferred by Theseus’s statement in Act 1.

The wedding arrangements were made in Athens and Theseus was set to marry Hippolyta, while at the same time offered to share their wedding with the two couples of; Hermia- Lysander and Demetrius - Helena.

What are Theseus and Hippolyta discussing at the start of A Midsummer Night's Dream?

Theseus is the Duke of Athens.  Hippolyta is the woman he is going to marry.  They are going to be married quite soon (4 more days) and that is what they are talking about when the play starts.

Specifically, the two of them are talking about how eager they are to get married.  They are really impatient for the four days to pass so that they can get married.

They only talk about this for a very little while in the first scene of the play.  Very soon, they are interrupted by Egeus, who has come to have Theseus lay down the law to Egeus's daughter, Hermia.

Describe Theseus and Hippolyta in A Midsummer Night's Dream.

Theseus is the duke of Athens. He is a very patriarchal male, meaning he firmly upholds a social order in which men have the preponderance of power. This is illustrated in how completely he supports Egeus's quest to marry his daughter Hermia to Demetrius. Hermia, who is in love with Lysander, protests vehemently against marrying a man she doesn't love, but Theseus tells her that

To you your father should be as a god

Theseus then tells Hermia that she will marry as her father wishes or choose between the death penalty and a convent.

Theseus also shows his patriarchal spirit in describing how he took Hippolyta against her will:

Hippolyta, I wooed thee with my sword
And won thy love doing thee injuries.

They're odd characters - only appearing at the start and at the end of the play. And it is the gap between these two appearances that seem to make the most difference to the way that they react to each other.

When they first enter, Theseus refers to having wooed Hippolyta (to whom he is to be married in a few days) "with my sword". He has conquered her in a war, and taken her as his bride. Those first lines of the play, before Egeus enters, are oddly transparent. Does Hippolyta resent her husband? Are the two in love? Is the conversation awkward? All interpretations can be played across the text.

It's not until 4.1 that the two appear again, now together outside, and hunting, Hippolyta making her famous comment on the music of the dogs' barking: "So musical a discord, such sweet thunder" (4.1.116-17). Happening upon the lovers, Theseus then over-rules Egeus and lifts the decree which insists that Hermia married Demetrius.

What has changed in the mean time which explains this personality change? Not a great deal, unless you argue that Hippolyta/Theseus have been "translated" (a key word in the play) into Titania/Oberon - and that their suppressed frustration in the first scene becomes the barely-controlled fury of Titania and Oberon's argument. But that's a different story.

Hippolyta and Theseus close the play watching the mechanicals' performance - though, as they head off to bed at the end, I'd conclude them, in the lovers' words, "strange and admirable" characters.

The roles of Theseus and Hippolyta in the Shakespearean comedy A Midsummer Night’s Dream involve authority, passivity, symbolism, and allusion.

Theseus’s role relates to power as Egeus goes to him when his daughter, Hermia, wants to marry Lysander instead of Demetrius. Theseus tries to talk some sense into her and seemingly has the authority to punish Hermia if she doesn’t comply with her father’s wishes. “Either to die the death or to abjure / For ever the society of men,” Theseus tells her. In other words, if Hermia continues to protest, she’ll either have to die or enter a nunnery. Theseus also symbolisms the extravagant role of courtship, as he announces, “Hippolyta, I woo’d thee with my sword, / And won thy love, doing thee injuries.” The theme of wooing and possessing plays a big role throughout the play.

As with Theseus, Hippolyta alludes to Greek mythology since Hippolyta was the queen of the Amazons—a tribe of female warriors. In Shakespeare’s comedy, Hippolyta’s role isn’t that of a warrior woman but a compliant wife. Thus, it’s possible to argue Hippolyta symbolizes the vanquished female who yields to male authority. At the same time, Hippolyta’s role might be to counter the rebellious role of Hermia. Unlike Hippolyta, Hermia doesn’t surrender to Theseus because she winds up with the person she wants to marry.